Seminar Event Detail

Abstract: Given a surface of finite type one can obtain a complex based on isotopy class of closed curves. This complex of curves is hyperbolic and has infinite diameter; as such it is natural to consider its boundary. Klarreich proved that the Gromov boundary of the complex of curves is the space of minimal foliations via a homeomorphism with electric Teichmuller space. In an effort to provide a more combinatorial proof Hamenstadt showed that the Gromov boundary of the complex of curves is homeomorphic to the space of filling minimal geodesic laminations. To do this she relied heavily on combinatorial properties of train tracks. In this talk I'll introduce train tracks and discuss their use in Hamenstadt's proof.